DeepCormack: Fermi surface tomography using model-based data-driven algorithms

2026-07-14

AI Summary

This study addresses the challenge of prohibitively long reconstruction times—often spanning several months—for three-dimensional two-photon momentum density (TPMD) in ACAR experiments due to low signal-to-noise ratios. To overcome this, the authors propose an efficient reconstruction framework that integrates physical modeling with deep learning. By combining the Cormack analytical formalism with neural architectures such as CNNs, MLPs, and U-Net, the method leverages singular value decomposition (SVD) and dynamic mode decomposition (DMD) to generate high-quality synthetic training data from a single reference momentum density derived from density functional theory (DFT). Requiring minimal experimental data, the approach enables sample-specific, high-fidelity, or accelerated TPMD reconstructions. At 200 million counts, it achieves approximately 8.5 dB higher peak signal-to-noise ratio (PSNR) than conventional techniques and remains robust under low-count conditions, potentially reducing data acquisition time from months to weeks.

Abstract

The experimental reconstruction of the 3D two-photon momentum density (TPMD) via angular correlation of electron-positron annihilation radiation (ACAR) is a particularly useful method for studying material Fermi surfaces. It does not rely on low temperatures, UHV conditions, or strong magnetic fields, and enables the study of the spin-resolved electronic structure of materials. Yet, it remains a challenging inverse problem. Typically, 10^8 positron annihilation events are measured for 3--6 projections of the TPMD at different angles. The standard reconstruction approach is an ACAR adaptation of Cormack's method (the MCM) that leverages the inherent symmetry in the crystal's structure. However, the poor signal-to-noise ratio means collecting data of sufficient quality for Fermi surface studies can take months per sample. We present DeepCormack, a family of data-driven model-based reconstruction algorithms that augments the MCM by integrating supervised deep-learning models (CNN, MLP, and UNet) at various stages. To overcome the lack of large experimental training sets, we propose a method which leverages singular value decomposition with dynamic mode decomposition to generate realistic synthetic TPMD volumes, requiring only a single reference momentum density computed via density functional theory. On test data, DeepCormack improves reconstruction quality over MCM by about 8.5 dB PSNR at 200M counts and remains stable at reduced counts, enabling significantly faster acquisition times. Generalisation to experimental data depends strongly on how well the training distribution from the reference momentum density matches the sample. We therefore recommend pairing DeepCormack with a DFT calculation of the target material to create sample-specific training data. Our proposed method offers either much higher quality reconstructions, or enables significantly faster ones, on the order of weeks.

Problem

• Fermi surface
• ACAR
• TPMD
• inverse problem
• signal-to-noise ratio

Innovation

• DeepCormack
• Fermi surface tomography
• ACAR
• data-driven reconstruction
• synthetic training data